Determining the Velocity Distribution Profile of a Fluid in an Inclined Flat Surface Using the Finite Element Method and the Exact Differential Equation Method

Abstract

An analysis has been carried out to determine the velocity profile of a fluid on an inclined plane using the Finite Element Method (FEM). The overall results from these finite elements were finally assembled to represent the velocity profile in the entire domain of the inclined plane. The results obtained from the finite element method shows that as the velocity distribution has a parabolic profile with the maximum velocity of 1109.8748m/s at open surface of the inclined plane. The fluid due to the no slip boundary condition has 0m/s at the walls of the inclined plane. Also, it was shown that the higher the angle of inclination and fluid viscosity, the lower the velocity and also the higher the fluid density, the higher the velocity. The result obtained from the FEM when compared with the result obtained from the exact differential equation method shows a strong agreement with a maximum percentage error of 2.3413x10-14 .